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sp_sm2_c64.c
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/* sp.c
*
* Copyright (C) 2006-2024 wolfSSL Inc.
*
* This file is part of wolfSSL.
*
* wolfSSL is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* wolfSSL is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
*/
/* Implementation by Sean Parkinson. */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <wolfssl/wolfcrypt/settings.h>
#if defined(WOLFSSL_HAVE_SP_RSA) || defined(WOLFSSL_HAVE_SP_DH) || \
defined(WOLFSSL_HAVE_SP_ECC)
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/cpuid.h>
#ifdef NO_INLINE
#include <wolfssl/wolfcrypt/misc.h>
#else
#define WOLFSSL_MISC_INCLUDED
#include <wolfcrypt/src/misc.c>
#endif
#ifdef RSA_LOW_MEM
#ifndef SP_RSA_PRIVATE_EXP_D
#define SP_RSA_PRIVATE_EXP_D
#endif
#ifndef WOLFSSL_SP_SMALL
#define WOLFSSL_SP_SMALL
#endif
#endif
#if defined(WOLFSSL_SMALL_STACK) && !defined(WOLFSSL_SP_NO_MALLOC)
#undef WOLFSSL_SP_SMALL_STACK
#define WOLFSSL_SP_SMALL_STACK
#endif
#include <wolfssl/wolfcrypt/sp.h>
#ifdef __IAR_SYSTEMS_ICC__
#define __asm__ asm
#define __volatile__ volatile
#define WOLFSSL_NO_VAR_ASSIGN_REG
#endif /* __IAR_SYSTEMS_ICC__ */
#ifdef __KEIL__
#define __asm__ __asm
#define __volatile__ volatile
#endif
#ifndef WOLFSSL_SP_ASM
#if SP_WORD_SIZE == 64
#define SP_PRINT_NUM(var, name, total, words, bits) \
do { \
int ii; \
byte nb[((bits) + 7) / 8]; \
sp_digit _s[words]; \
XMEMCPY(_s, var, sizeof(_s)); \
sp_##total##_norm_##words(_s); \
sp_##total##_to_bin_##words(_s, nb); \
fprintf(stderr, name "=0x"); \
for (ii=0; ii<((bits) + 7) / 8; ii++) \
fprintf(stderr, "%02x", nb[ii]); \
fprintf(stderr, "\n"); \
} while (0)
#define SP_PRINT_VAL(var, name) \
fprintf(stderr, name "=0x" SP_PRINT_FMT "\n", var)
#define SP_PRINT_INT(var, name) \
fprintf(stderr, name "=%d\n", var)
#if defined(WOLFSSL_SP_SMALL) && defined(WOLFSSL_SP_SM2)
/* Mask for address to obfuscate which of the two address will be used. */
static const size_t addr_mask[2] = { 0, (size_t)-1 };
#endif
#if defined(WOLFSSL_SP_NONBLOCK) && (!defined(WOLFSSL_SP_NO_MALLOC) || \
!defined(WOLFSSL_SP_SMALL))
#error SP non-blocking requires small and no-malloc (WOLFSSL_SP_SMALL and WOLFSSL_SP_NO_MALLOC)
#endif
#ifdef WOLFSSL_HAVE_SP_ECC
#ifdef WOLFSSL_SP_SM2
/* Point structure to use. */
typedef struct sp_point_256 {
/* X ordinate of point. */
sp_digit x[2 * 5];
/* Y ordinate of point. */
sp_digit y[2 * 5];
/* Z ordinate of point. */
sp_digit z[2 * 5];
/* Indicates point is at infinity. */
int infinity;
} sp_point_256;
/* The modulus (prime) of the curve SM2 P256. */
static const sp_digit p256_sm2_mod[5] = {
0xfffffffffffffL,0xff00000000fffL,0xfffffffffffffL,0xfffffffffffffL,
0x0fffffffeffffL
};
/* The Montgomery normalizer for modulus of the curve P256. */
static const sp_digit p256_sm2_norm_mod[5] = {
0x0000000000001L,0x00ffffffff000L,0x0000000000000L,0x0000000000000L,
0x0000000010000L
};
/* The Montgomery multiplier for modulus of the curve P256. */
static const sp_digit p256_sm2_mp_mod = 0x0000000000001;
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || defined(HAVE_ECC_SIGN) || \
defined(HAVE_ECC_VERIFY)
/* The order of the curve P256. */
static const sp_digit p256_sm2_order[5] = {
0xbf40939d54123L,0x6b21c6052b53bL,0xfffffff7203dfL,0xfffffffffffffL,
0x0fffffffeffffL
};
#endif
/* The order of the curve P256 minus 2. */
static const sp_digit p256_sm2_order2[5] = {
0xbf40939d54121L,0x6b21c6052b53bL,0xfffffff7203dfL,0xfffffffffffffL,
0x0fffffffeffffL
};
#if defined(HAVE_ECC_SIGN)
/* The Montgomery normalizer for order of the curve P256. */
static const sp_digit p256_sm2_norm_order[5] = {
0x40bf6c62abeddL,0x94de39fad4ac4L,0x00000008dfc20L,0x0000000000000L,
0x0000000010000L
};
#endif
#if defined(HAVE_ECC_SIGN)
/* The Montgomery multiplier for order of the curve P256. */
static const sp_digit p256_sm2_mp_order = 0xf9e8872350975L;
#endif
/* The base point of curve P256. */
static const sp_point_256 p256_sm2_base = {
/* X ordinate */
{
0xa4589334c74c7L,0xbff2660be1715L,0xa39c9948fe30bL,0x81195f9904466L,
0x032c4ae2c1f19L,
(sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0
},
/* Y ordinate */
{
0xf32e52139f0a0L,0x7cc62a474002dL,0xb692153d0a987L,0x779c59bdcee36L,
0x0bc3736a2f4f6L,
(sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0
},
/* Z ordinate */
{
0x0000000000001L,0x0000000000000L,0x0000000000000L,0x0000000000000L,
0x0000000000000L,
(sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0, (sp_digit)0
},
/* infinity */
0
};
#if defined(HAVE_ECC_CHECK_KEY) || defined(HAVE_COMP_KEY)
static const sp_digit p256_sm2_b[5] = {
0xcbd414d940e93L,0xf515ab8f92ddbL,0xf6509a7f39789L,0x5e344d5a9e4bcL,
0x028e9fa9e9d9fL
};
#endif
#ifdef WOLFSSL_SP_SMALL
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
int imax;
int k;
sp_uint128 c;
sp_uint128 lo;
c = ((sp_uint128)a[4]) * b[4];
r[9] = (sp_digit)(c >> 52);
c &= 0xfffffffffffffL;
for (k = 7; k >= 0; k--) {
if (k >= 5) {
i = k - 4;
imax = 4;
}
else {
i = 0;
imax = k;
}
lo = 0;
for (; i <= imax; i++) {
lo += ((sp_uint128)a[i]) * b[k - i];
}
c += lo >> 52;
r[k + 2] += (sp_digit)(c >> 52);
r[k + 1] = (sp_digit)(c & 0xfffffffffffffL);
c = lo & 0xfffffffffffffL;
}
r[0] = (sp_digit)c;
}
#else
/* Multiply a and b into r. (r = a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static void sp_256_mul_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
sp_int128 t0 = ((sp_int128)a[ 0]) * b[ 0];
sp_int128 t1 = ((sp_int128)a[ 0]) * b[ 1]
+ ((sp_int128)a[ 1]) * b[ 0];
sp_int128 t2 = ((sp_int128)a[ 0]) * b[ 2]
+ ((sp_int128)a[ 1]) * b[ 1]
+ ((sp_int128)a[ 2]) * b[ 0];
sp_int128 t3 = ((sp_int128)a[ 0]) * b[ 3]
+ ((sp_int128)a[ 1]) * b[ 2]
+ ((sp_int128)a[ 2]) * b[ 1]
+ ((sp_int128)a[ 3]) * b[ 0];
sp_int128 t4 = ((sp_int128)a[ 0]) * b[ 4]
+ ((sp_int128)a[ 1]) * b[ 3]
+ ((sp_int128)a[ 2]) * b[ 2]
+ ((sp_int128)a[ 3]) * b[ 1]
+ ((sp_int128)a[ 4]) * b[ 0];
sp_int128 t5 = ((sp_int128)a[ 1]) * b[ 4]
+ ((sp_int128)a[ 2]) * b[ 3]
+ ((sp_int128)a[ 3]) * b[ 2]
+ ((sp_int128)a[ 4]) * b[ 1];
sp_int128 t6 = ((sp_int128)a[ 2]) * b[ 4]
+ ((sp_int128)a[ 3]) * b[ 3]
+ ((sp_int128)a[ 4]) * b[ 2];
sp_int128 t7 = ((sp_int128)a[ 3]) * b[ 4]
+ ((sp_int128)a[ 4]) * b[ 3];
sp_int128 t8 = ((sp_int128)a[ 4]) * b[ 4];
t1 += t0 >> 52; r[ 0] = t0 & 0xfffffffffffffL;
t2 += t1 >> 52; r[ 1] = t1 & 0xfffffffffffffL;
t3 += t2 >> 52; r[ 2] = t2 & 0xfffffffffffffL;
t4 += t3 >> 52; r[ 3] = t3 & 0xfffffffffffffL;
t5 += t4 >> 52; r[ 4] = t4 & 0xfffffffffffffL;
t6 += t5 >> 52; r[ 5] = t5 & 0xfffffffffffffL;
t7 += t6 >> 52; r[ 6] = t6 & 0xfffffffffffffL;
t8 += t7 >> 52; r[ 7] = t7 & 0xfffffffffffffL;
r[9] = (sp_digit)(t8 >> 52);
r[8] = t8 & 0xfffffffffffffL;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_sm2_5(sp_digit* r, const sp_digit* a)
{
int i;
int imax;
int k;
sp_uint128 c;
sp_uint128 t;
c = ((sp_uint128)a[4]) * a[4];
r[9] = (sp_digit)(c >> 52);
c = (c & 0xfffffffffffffL) << 52;
for (k = 7; k >= 0; k--) {
i = (k + 1) / 2;
if ((k & 1) == 0) {
c += ((sp_uint128)a[i]) * a[i];
i++;
}
if (k < 4) {
imax = k;
}
else {
imax = 4;
}
t = 0;
for (; i <= imax; i++) {
t += ((sp_uint128)a[i]) * a[k - i];
}
c += t * 2;
r[k + 2] += (sp_digit) (c >> 104);
r[k + 1] = (sp_digit)((c >> 52) & 0xfffffffffffffL);
c = (c & 0xfffffffffffffL) << 52;
}
r[0] = (sp_digit)(c >> 52);
}
#else
/* Square a and put result in r. (r = a * a)
*
* r A single precision integer.
* a A single precision integer.
*/
SP_NOINLINE static void sp_256_sqr_sm2_5(sp_digit* r, const sp_digit* a)
{
sp_int128 t0 = ((sp_int128)a[ 0]) * a[ 0];
sp_int128 t1 = (((sp_int128)a[ 0]) * a[ 1]) * 2;
sp_int128 t2 = (((sp_int128)a[ 0]) * a[ 2]) * 2
+ ((sp_int128)a[ 1]) * a[ 1];
sp_int128 t3 = (((sp_int128)a[ 0]) * a[ 3]
+ ((sp_int128)a[ 1]) * a[ 2]) * 2;
sp_int128 t4 = (((sp_int128)a[ 0]) * a[ 4]
+ ((sp_int128)a[ 1]) * a[ 3]) * 2
+ ((sp_int128)a[ 2]) * a[ 2];
sp_int128 t5 = (((sp_int128)a[ 1]) * a[ 4]
+ ((sp_int128)a[ 2]) * a[ 3]) * 2;
sp_int128 t6 = (((sp_int128)a[ 2]) * a[ 4]) * 2
+ ((sp_int128)a[ 3]) * a[ 3];
sp_int128 t7 = (((sp_int128)a[ 3]) * a[ 4]) * 2;
sp_int128 t8 = ((sp_int128)a[ 4]) * a[ 4];
t1 += t0 >> 52; r[ 0] = t0 & 0xfffffffffffffL;
t2 += t1 >> 52; r[ 1] = t1 & 0xfffffffffffffL;
t3 += t2 >> 52; r[ 2] = t2 & 0xfffffffffffffL;
t4 += t3 >> 52; r[ 3] = t3 & 0xfffffffffffffL;
t5 += t4 >> 52; r[ 4] = t4 & 0xfffffffffffffL;
t6 += t5 >> 52; r[ 5] = t5 & 0xfffffffffffffL;
t7 += t6 >> 52; r[ 6] = t6 & 0xfffffffffffffL;
t8 += t7 >> 52; r[ 7] = t7 & 0xfffffffffffffL;
r[9] = (sp_digit)(t8 >> 52);
r[8] = t8 & 0xfffffffffffffL;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 5; i++) {
r[i] = a[i] + b[i];
}
return 0;
}
#else
/* Add b to a into r. (r = a + b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_add_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] + b[ 0];
r[ 1] = a[ 1] + b[ 1];
r[ 2] = a[ 2] + b[ 2];
r[ 3] = a[ 3] + b[ 3];
r[ 4] = a[ 4] + b[ 4];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
int i;
for (i = 0; i < 5; i++) {
r[i] = a[i] - b[i];
}
return 0;
}
#else
/* Sub b from a into r. (r = a - b)
*
* r A single precision integer.
* a A single precision integer.
* b A single precision integer.
*/
SP_NOINLINE static int sp_256_sub_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b)
{
r[ 0] = a[ 0] - b[ 0];
r[ 1] = a[ 1] - b[ 1];
r[ 2] = a[ 2] - b[ 2];
r[ 3] = a[ 3] - b[ 3];
r[ 4] = a[ 4] - b[ 4];
return 0;
}
#endif /* WOLFSSL_SP_SMALL */
/* Convert an mp_int to an array of sp_digit.
*
* r A single precision integer.
* size Maximum number of bytes to convert
* a A multi-precision integer.
*/
static void sp_256_from_mp(sp_digit* r, int size, const mp_int* a)
{
#if DIGIT_BIT == 52
int i;
sp_digit j = (sp_digit)0 - (sp_digit)a->used;
int o = 0;
for (i = 0; i < size; i++) {
sp_digit mask = (sp_digit)0 - (j >> 51);
r[i] = a->dp[o] & mask;
j++;
o += (int)(j >> 51);
}
#elif DIGIT_BIT > 52
unsigned int i;
int j = 0;
word32 s = 0;
r[0] = 0;
for (i = 0; i < (unsigned int)a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i] << s);
r[j] &= 0xfffffffffffffL;
s = 52U - s;
if (j + 1 >= size) {
break;
}
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
while ((s + 52U) <= (word32)DIGIT_BIT) {
s += 52U;
r[j] &= 0xfffffffffffffL;
if (j + 1 >= size) {
break;
}
if (s < (word32)DIGIT_BIT) {
/* lint allow cast of mismatch word32 and mp_digit */
r[++j] = (sp_digit)(a->dp[i] >> s); /*lint !e9033*/
}
else {
r[++j] = (sp_digit)0;
}
}
s = (word32)DIGIT_BIT - s;
}
for (j++; j < size; j++) {
r[j] = 0;
}
#else
unsigned int i;
int j = 0;
int s = 0;
r[0] = 0;
for (i = 0; i < (unsigned int)a->used && j < size; i++) {
r[j] |= ((sp_digit)a->dp[i]) << s;
if (s + DIGIT_BIT >= 52) {
r[j] &= 0xfffffffffffffL;
if (j + 1 >= size) {
break;
}
s = 52 - s;
if (s == DIGIT_BIT) {
r[++j] = 0;
s = 0;
}
else {
r[++j] = a->dp[i] >> s;
s = DIGIT_BIT - s;
}
}
else {
s += DIGIT_BIT;
}
}
for (j++; j < size; j++) {
r[j] = 0;
}
#endif
}
/* Convert a point of type ecc_point to type sp_point_256.
*
* p Point of type sp_point_256 (result).
* pm Point of type ecc_point.
*/
static void sp_256_point_from_ecc_point_5(sp_point_256* p,
const ecc_point* pm)
{
XMEMSET(p->x, 0, sizeof(p->x));
XMEMSET(p->y, 0, sizeof(p->y));
XMEMSET(p->z, 0, sizeof(p->z));
sp_256_from_mp(p->x, 5, pm->x);
sp_256_from_mp(p->y, 5, pm->y);
sp_256_from_mp(p->z, 5, pm->z);
p->infinity = 0;
}
/* Convert an array of sp_digit to an mp_int.
*
* a A single precision integer.
* r A multi-precision integer.
*/
static int sp_256_to_mp(const sp_digit* a, mp_int* r)
{
int err;
err = mp_grow(r, (256 + DIGIT_BIT - 1) / DIGIT_BIT);
if (err == MP_OKAY) { /*lint !e774 case where err is always MP_OKAY*/
#if DIGIT_BIT == 52
XMEMCPY(r->dp, a, sizeof(sp_digit) * 5);
r->used = 5;
mp_clamp(r);
#elif DIGIT_BIT < 52
int i;
int j = 0;
int s = 0;
r->dp[0] = 0;
for (i = 0; i < 5; i++) {
r->dp[j] |= (mp_digit)(a[i] << s);
r->dp[j] &= ((sp_digit)1 << DIGIT_BIT) - 1;
s = DIGIT_BIT - s;
r->dp[++j] = (mp_digit)(a[i] >> s);
while (s + DIGIT_BIT <= 52) {
s += DIGIT_BIT;
r->dp[j++] &= ((sp_digit)1 << DIGIT_BIT) - 1;
if (s == SP_WORD_SIZE) {
r->dp[j] = 0;
}
else {
r->dp[j] = (mp_digit)(a[i] >> s);
}
}
s = 52 - s;
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#else
int i;
int j = 0;
int s = 0;
r->dp[0] = 0;
for (i = 0; i < 5; i++) {
r->dp[j] |= ((mp_digit)a[i]) << s;
if (s + 52 >= DIGIT_BIT) {
#if DIGIT_BIT != 32 && DIGIT_BIT != 64
r->dp[j] &= ((sp_digit)1 << DIGIT_BIT) - 1;
#endif
s = DIGIT_BIT - s;
r->dp[++j] = a[i] >> s;
s = 52 - s;
}
else {
s += 52;
}
}
r->used = (256 + DIGIT_BIT - 1) / DIGIT_BIT;
mp_clamp(r);
#endif
}
return err;
}
/* Convert a point of type sp_point_256 to type ecc_point.
*
* p Point of type sp_point_256.
* pm Point of type ecc_point (result).
* returns MEMORY_E when allocation of memory in ecc_point fails otherwise
* MP_OKAY.
*/
static int sp_256_point_to_ecc_point_5(const sp_point_256* p, ecc_point* pm)
{
int err;
err = sp_256_to_mp(p->x, pm->x);
if (err == MP_OKAY) {
err = sp_256_to_mp(p->y, pm->y);
}
if (err == MP_OKAY) {
err = sp_256_to_mp(p->z, pm->z);
}
return err;
}
#define sp_256_mont_reduce_order_sm2_5 sp_256_mont_reduce_sm2_5
/* Compare a with b in constant time.
*
* a A single precision integer.
* b A single precision integer.
* return -ve, 0 or +ve if a is less than, equal to or greater than b
* respectively.
*/
static sp_digit sp_256_cmp_sm2_5(const sp_digit* a, const sp_digit* b)
{
sp_digit r = 0;
#ifdef WOLFSSL_SP_SMALL
int i;
for (i=4; i>=0; i--) {
r |= (a[i] - b[i]) & ~(((sp_digit)0 - r) >> 51);
}
#else
r |= (a[ 4] - b[ 4]) & (0 - (sp_digit)1);
r |= (a[ 3] - b[ 3]) & ~(((sp_digit)0 - r) >> 51);
r |= (a[ 2] - b[ 2]) & ~(((sp_digit)0 - r) >> 51);
r |= (a[ 1] - b[ 1]) & ~(((sp_digit)0 - r) >> 51);
r |= (a[ 0] - b[ 0]) & ~(((sp_digit)0 - r) >> 51);
#endif /* WOLFSSL_SP_SMALL */
return r;
}
/* Conditionally subtract b from a using the mask m.
* m is -1 to subtract and 0 when not.
*
* r A single precision number representing condition subtract result.
* a A single precision number to subtract from.
* b A single precision number to subtract.
* m Mask value to apply.
*/
static void sp_256_cond_sub_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit m)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 5; i++) {
r[i] = a[i] - (b[i] & m);
}
#else
r[ 0] = a[ 0] - (b[ 0] & m);
r[ 1] = a[ 1] - (b[ 1] & m);
r[ 2] = a[ 2] - (b[ 2] & m);
r[ 3] = a[ 3] - (b[ 3] & m);
r[ 4] = a[ 4] - (b[ 4] & m);
#endif /* WOLFSSL_SP_SMALL */
}
/* Mul a by scalar b and add into r. (r += a * b)
*
* r A single precision integer.
* a A single precision integer.
* b A scalar.
*/
SP_NOINLINE static void sp_256_mul_add_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit b)
{
#ifdef WOLFSSL_SP_SMALL
sp_int128 tb = b;
sp_int128 t[4];
int i;
t[0] = 0;
for (i = 0; i < 4; i += 4) {
t[0] += (tb * a[i+0]) + r[i+0];
t[1] = (tb * a[i+1]) + r[i+1];
t[2] = (tb * a[i+2]) + r[i+2];
t[3] = (tb * a[i+3]) + r[i+3];
r[i+0] = t[0] & 0xfffffffffffffL;
t[1] += t[0] >> 52;
r[i+1] = t[1] & 0xfffffffffffffL;
t[2] += t[1] >> 52;
r[i+2] = t[2] & 0xfffffffffffffL;
t[3] += t[2] >> 52;
r[i+3] = t[3] & 0xfffffffffffffL;
t[0] = t[3] >> 52;
}
t[0] += (tb * a[4]) + r[4];
r[4] = t[0] & 0xfffffffffffffL;
r[5] += (sp_digit)(t[0] >> 52);
#else
sp_int128 tb = b;
sp_int128 t[5];
t[ 0] = tb * a[ 0];
t[ 1] = tb * a[ 1];
t[ 2] = tb * a[ 2];
t[ 3] = tb * a[ 3];
t[ 4] = tb * a[ 4];
r[ 0] += (sp_digit) (t[ 0] & 0xfffffffffffffL);
r[ 1] += (sp_digit)((t[ 0] >> 52) + (t[ 1] & 0xfffffffffffffL));
r[ 2] += (sp_digit)((t[ 1] >> 52) + (t[ 2] & 0xfffffffffffffL));
r[ 3] += (sp_digit)((t[ 2] >> 52) + (t[ 3] & 0xfffffffffffffL));
r[ 4] += (sp_digit)((t[ 3] >> 52) + (t[ 4] & 0xfffffffffffffL));
r[ 5] += (sp_digit) (t[ 4] >> 52);
#endif /* WOLFSSL_SP_SMALL */
}
/* Normalize the values in each word to 52 bits.
*
* a Array of sp_digit to normalize.
*/
static void sp_256_norm_5(sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
for (i = 0; i < 4; i++) {
a[i+1] += a[i] >> 52;
a[i] &= 0xfffffffffffffL;
}
#else
a[1] += a[0] >> 52; a[0] &= 0xfffffffffffffL;
a[2] += a[1] >> 52; a[1] &= 0xfffffffffffffL;
a[3] += a[2] >> 52; a[2] &= 0xfffffffffffffL;
a[4] += a[3] >> 52; a[3] &= 0xfffffffffffffL;
#endif /* WOLFSSL_SP_SMALL */
}
/* Shift the result in the high 256 bits down to the bottom.
*
* r A single precision number.
* a A single precision number.
*/
static void sp_256_mont_shift_5(sp_digit* r, const sp_digit* a)
{
#ifdef WOLFSSL_SP_SMALL
int i;
sp_uint64 n;
n = a[4] >> 48;
for (i = 0; i < 4; i++) {
n += (sp_uint64)a[5 + i] << 4;
r[i] = n & 0xfffffffffffffL;
n >>= 52;
}
n += (sp_uint64)a[9] << 4;
r[4] = n;
#else
sp_uint64 n;
n = a[4] >> 48;
n += (sp_uint64)a[ 5] << 4U; r[ 0] = n & 0xfffffffffffffUL; n >>= 52U;
n += (sp_uint64)a[ 6] << 4U; r[ 1] = n & 0xfffffffffffffUL; n >>= 52U;
n += (sp_uint64)a[ 7] << 4U; r[ 2] = n & 0xfffffffffffffUL; n >>= 52U;
n += (sp_uint64)a[ 8] << 4U; r[ 3] = n & 0xfffffffffffffUL; n >>= 52U;
n += (sp_uint64)a[ 9] << 4U; r[ 4] = n;
#endif /* WOLFSSL_SP_SMALL */
XMEMSET(&r[5], 0, sizeof(*r) * 5U);
}
/* Reduce the number back to 256 bits using Montgomery reduction.
*
* a A single precision number to reduce in place.
* m The single precision number representing the modulus.
* mp The digit representing the negative inverse of m mod 2^n.
*/
static void sp_256_mont_reduce_sm2_5(sp_digit* a, const sp_digit* m, sp_digit mp)
{
int i;
sp_digit mu;
if (mp != 1) {
for (i=0; i<4; i++) {
mu = (a[i] * mp) & 0xfffffffffffffL;
sp_256_mul_add_sm2_5(a+i, m, mu);
a[i+1] += a[i] >> 52;
}
mu = (a[i] * mp) & 0xffffffffffffL;
sp_256_mul_add_sm2_5(a+i, m, mu);
a[i+1] += a[i] >> 52;
a[i] &= 0xfffffffffffffL;
}
else {
for (i=0; i<4; i++) {
mu = a[i] & 0xfffffffffffffL;
sp_256_mul_add_sm2_5(a+i, p256_sm2_mod, mu);
a[i+1] += a[i] >> 52;
}
mu = a[i] & 0xffffffffffffL;
sp_256_mul_add_sm2_5(a+i, p256_sm2_mod, mu);
a[i+1] += a[i] >> 52;
a[i] &= 0xfffffffffffffL;
}
sp_256_mont_shift_5(a, a);
sp_256_cond_sub_sm2_5(a, a, m, 0 - (((a[4] >> 48) > 0) ?
(sp_digit)1 : (sp_digit)0));
sp_256_norm_5(a);
}
/* Multiply two Montgomery form numbers mod the modulus (prime).
* (r = a * b mod m)
*
* r Result of multiplication.
* a First number to multiply in Montgomery form.
* b Second number to multiply in Montgomery form.
* m Modulus (prime).
* mp Montgomery multiplier.
*/
SP_NOINLINE static void sp_256_mont_mul_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* b, const sp_digit* m, sp_digit mp)
{
sp_256_mul_sm2_5(r, a, b);
sp_256_mont_reduce_sm2_5(r, m, mp);
}
/* Square the Montgomery form number. (r = a * a mod m)
*
* r Result of squaring.
* a Number to square in Montgomery form.
* m Modulus (prime).
* mp Montgomery multiplier.
*/
SP_NOINLINE static void sp_256_mont_sqr_sm2_5(sp_digit* r, const sp_digit* a,
const sp_digit* m, sp_digit mp)
{
sp_256_sqr_sm2_5(r, a);
sp_256_mont_reduce_sm2_5(r, m, mp);
}
#if !defined(WOLFSSL_SP_SMALL)
/* Square the Montgomery form number a number of times. (r = a ^ n mod m)
*
* r Result of squaring.
* a Number to square in Montgomery form.
* n Number of times to square.
* m Modulus (prime).
* mp Montgomery multiplier.
*/
SP_NOINLINE static void sp_256_mont_sqr_n_sm2_5(sp_digit* r,
const sp_digit* a, int n, const sp_digit* m, sp_digit mp)
{
sp_256_mont_sqr_sm2_5(r, a, m, mp);
for (; n > 1; n--) {
sp_256_mont_sqr_sm2_5(r, r, m, mp);
}
}
#endif /* !WOLFSSL_SP_SMALL */
#ifdef WOLFSSL_SP_SMALL
/* Mod-2 for the SM2 P256 curve. */
static const uint64_t p256_sm2_mod_minus_2[4] = {
0xfffffffffffffffdU,0xffffffff00000000U,0xffffffffffffffffU,
0xfffffffeffffffffU
};
#endif /* !WOLFSSL_SP_SMALL */
/* Invert the number, in Montgomery form, modulo the modulus (prime) of the
* P256 curve. (r = 1 / a mod m)
*
* r Inverse result.
* a Number to invert.
* td Temporary data.
*/
static void sp_256_mont_inv_sm2_5(sp_digit* r, const sp_digit* a, sp_digit* td)
{
#ifdef WOLFSSL_SP_SMALL
sp_digit* t = td;
int i;
XMEMCPY(t, a, sizeof(sp_digit) * 5);
for (i=254; i>=0; i--) {
sp_256_mont_sqr_sm2_5(t, t, p256_sm2_mod, p256_sm2_mp_mod);
if (p256_sm2_mod_minus_2[i / 64] & ((sp_digit)1 << (i % 64)))
sp_256_mont_mul_sm2_5(t, t, a, p256_sm2_mod, p256_sm2_mp_mod);
}
XMEMCPY(r, t, sizeof(sp_digit) * 5);
#else
sp_digit* t1 = td;
sp_digit* t2 = td + 2 * 5;
sp_digit* t3 = td + 4 * 5;
sp_digit* t4 = td + 6 * 5;
/* 0x2 */
sp_256_mont_sqr_sm2_5(t1, a, p256_sm2_mod, p256_sm2_mp_mod);
/* 0x3 */
sp_256_mont_mul_sm2_5(t2, t1, a, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xc */
sp_256_mont_sqr_n_sm2_5(t1, t2, 2, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xd */
sp_256_mont_mul_sm2_5(t3, t1, a, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xf */
sp_256_mont_mul_sm2_5(t2, t2, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xf0 */
sp_256_mont_sqr_n_sm2_5(t1, t2, 4, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfd */
sp_256_mont_mul_sm2_5(t3, t3, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xff */
sp_256_mont_mul_sm2_5(t2, t2, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xff00 */
sp_256_mont_sqr_n_sm2_5(t1, t2, 8, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffd */
sp_256_mont_mul_sm2_5(t3, t3, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xffff */
sp_256_mont_mul_sm2_5(t2, t2, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xffff0000 */
sp_256_mont_sqr_n_sm2_5(t1, t2, 16, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffd */
sp_256_mont_mul_sm2_5(t3, t3, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffe */
sp_256_mont_mul_sm2_5(t2, t3, a, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xffffffff */
sp_256_mont_mul_sm2_5(t4, t2, a, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffe00000000 */
sp_256_mont_sqr_n_sm2_5(t2, t2, 32, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffff */
sp_256_mont_mul_sm2_5(t2, t4, t2, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffff00000000 */
sp_256_mont_sqr_n_sm2_5(t1, t2, 32, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffff */
sp_256_mont_mul_sm2_5(r, t4, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffff00000000 */
sp_256_mont_sqr_n_sm2_5(t1, r, 32, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffff */
sp_256_mont_mul_sm2_5(r, t4, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffff00000000 */
sp_256_mont_sqr_n_sm2_5(r, r, 32, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffffffffffff */
sp_256_mont_mul_sm2_5(r, r, t4, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffffffffffff0000000000000000 */
sp_256_mont_sqr_n_sm2_5(r, r, 64, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffff */
sp_256_mont_mul_sm2_5(r, r, t4, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffff00000000 */
sp_256_mont_sqr_n_sm2_5(r, r, 32, p256_sm2_mod, p256_sm2_mp_mod);
/* 0xfffffffeffffffffffffffffffffffffffffffff00000000fffffffffffffffd */
sp_256_mont_mul_sm2_5(r, r, t3, p256_sm2_mod, p256_sm2_mp_mod);
#endif /* WOLFSSL_SP_SMALL */
}
/* Map the Montgomery form projective coordinate point to an affine point.
*
* r Resulting affine coordinate point.
* p Montgomery form projective coordinate point.
* t Temporary ordinate data.
*/
static void sp_256_map_sm2_5(sp_point_256* r, const sp_point_256* p,
sp_digit* t)
{
sp_digit* t1 = t;
sp_digit* t2 = t + 2*5;
sp_int64 n;
sp_256_mont_inv_sm2_5(t1, p->z, t + 2*5);
sp_256_mont_sqr_sm2_5(t2, t1, p256_sm2_mod, p256_sm2_mp_mod);
sp_256_mont_mul_sm2_5(t1, t2, t1, p256_sm2_mod, p256_sm2_mp_mod);
/* x /= z^2 */
sp_256_mont_mul_sm2_5(r->x, p->x, t2, p256_sm2_mod, p256_sm2_mp_mod);
XMEMSET(r->x + 5, 0, sizeof(sp_digit) * 5U);
sp_256_mont_reduce_sm2_5(r->x, p256_sm2_mod, p256_sm2_mp_mod);
/* Reduce x to less than modulus */
n = sp_256_cmp_sm2_5(r->x, p256_sm2_mod);
sp_256_cond_sub_sm2_5(r->x, r->x, p256_sm2_mod, (sp_digit)~(n >> 51));
sp_256_norm_5(r->x);
/* y /= z^3 */
sp_256_mont_mul_sm2_5(r->y, p->y, t1, p256_sm2_mod, p256_sm2_mp_mod);
XMEMSET(r->y + 5, 0, sizeof(sp_digit) * 5U);
sp_256_mont_reduce_sm2_5(r->y, p256_sm2_mod, p256_sm2_mp_mod);
/* Reduce y to less than modulus */
n = sp_256_cmp_sm2_5(r->y, p256_sm2_mod);
sp_256_cond_sub_sm2_5(r->y, r->y, p256_sm2_mod, (sp_digit)~(n >> 51));
sp_256_norm_5(r->y);
XMEMSET(r->z, 0, sizeof(r->z) / 2);
r->z[0] = 1;
}
/* Add two Montgomery form numbers (r = a + b % m).
*
* r Result of addition.